Arrange selected vertices in a curved shape
Another option is:


removing the row of vertices you want to make curved
adding a Bezier curve in its place. 

"Resolution Preview U" should be set to exactly $N-1$ where $N$ is the number of vertices making a side of your cube.

Also, you might want to make sure that the Bezier curve lays completely on the XY plane
converting the curve to mesh
joining the curve and the cube
reconstructing the faces by selecting the two adjacent rows and doing "Bridge Edge Loops" (must be done once per side)